They plan to give token holders an additional 999 PXS for every 1 PXS they already hold. However the current total supply of 36,104,947.59 PXS would not be nearly enough to cover the number of additional tokens required:

I can't imagine that it would be possible for them to retroactively increase the total supply of an ERC20 token. Is this possible or would they have to create a second token with 1000x supply and airdrop this on a 1000:1 ratio to current token holders instead?

3 Answers
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A "mintable" token has a function that lets the "minter" issue new tokens. It's simple arithmetic that increases the total supply and credits the new tokens to an address - usually the minter.

Functions can't be added to contracts after deployment.

So, if there is no minter function in a deployed contract, then the total supply can't be increased. If there is a minter function, then the author has reserved the option of increasing supply in the future.

In practice, mintable token contracts often implement an irreversible OFF switch. The minter can set the switch to indicate that minting is over at such time as they want to demonstrate that no further issuance is possible. For example, a flag - isMintable = false.